Method and apparatus for video coding

ABSTRACT

Aspects of the disclosure provide an apparatus that includes processing circuitry and a method for video decoding. The processing circuitry decodes coding information of a block to be reconstructed from a coded video bitstream. The coding information indicates intra prediction information for the block. For the block coded with a directional mode, the processing circuitry determines the directional mode based on a nominal mode and an angular offset. The coding information indicates the nominal mode and the angular offset. The processing circuitry determines a non-separable transform for the block based on the nominal mode, and reconstructs the block based on the directional mode and the non-separable transform. In an example, the processing circuitry determines a transform set mode that is associated with the nominal mode, and the transform set mode indicates a set of one or more non-separable transforms that includes the non-separable transform.

INCORPORATION BY REFERENCE

This present disclosure claims the benefit of priority to U.S.Provisional Application No. 62/941,359, “Secondary Transform for IntraCoding” filed on Nov. 27, 2019, which is incorporated by referenceherein in its entirety.

TECHNICAL FIELD

The present disclosure describes embodiments generally related to videocoding.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Video encoding and decoding can be performed using inter-pictureprediction with motion compensation. Uncompressed digital video caninclude a series of pictures, each picture having a spatial dimensionof, for example, 1920×1080 luminance samples and associated chrominancesamples. The series of pictures can have a fixed or variable picturerate (informally also known as frame rate), of, for example 60 picturesper second or 60 Hz. Uncompressed video has specific bitraterequirements. For example, 1080p60 4:2:0 video at 8 bit per sample(1920×1080 luminance sample resolution at 60 Hz frame rate) requiresclose to 1.5 Gbit/s bandwidth. An hour of such video requires more than600 GBytes of storage space.

One purpose of video coding and decoding can be the reduction ofredundancy in the input video signal, through compression. Compressioncan help reduce the aforementioned bandwidth and/or storage spacerequirements, in some cases by two orders of magnitude or more. Bothlossless compression and lossy compression, as well as a combinationthereof can be employed. Lossless compression refers to techniques wherean exact copy of the original signal can be reconstructed from thecompressed original signal. When using lossy compression, thereconstructed signal may not be identical to the original signal, butthe distortion between original and reconstructed signals is smallenough to make the reconstructed signal useful for the intendedapplication. In the case of video, lossy compression is widely employed.The amount of distortion tolerated depends on the application; forexample, users of certain consumer streaming applications may toleratehigher distortion than users of television distribution applications.The compression ratio achievable can reflect that: higherallowable/tolerable distortion can yield higher compression ratios.

A video encoder and decoder can utilize techniques from several broadcategories, including, for example, motion compensation, transform,quantization, and entropy coding.

Video codec technologies can include techniques known as intra coding.In intra coding, sample values are represented without reference tosamples or other data from previously reconstructed reference pictures.In some video codecs, the picture is spatially subdivided into blocks ofsamples. When all blocks of samples are coded in intra mode, thatpicture can be an intra picture. Intra pictures and their derivationssuch as independent decoder refresh pictures, can be used to reset thedecoder state and can, therefore, be used as the first picture in acoded video bitstream and a video session, or as a still image. Thesamples of an intra block can be exposed to a transform, and thetransform coefficients can be quantized before entropy coding. Intraprediction can be a technique that minimizes sample values in thepre-transform domain. In some cases, the smaller the DC value after atransform is, and the smaller the AC coefficients are, the fewer thebits that are required at a given quantization step size to representthe block after entropy coding.

Traditional intra coding such as known from, for example MPEG-2generation coding technologies, does not use intra prediction. However,some newer video compression technologies include techniques thatattempt, from, for example, surrounding sample data and/or metadataobtained during the encoding/decoding of spatially neighboring, andpreceding in decoding order, blocks of data. Such techniques arehenceforth called “intra prediction” techniques. Note that in at leastsome cases, intra prediction is using reference data only from thecurrent picture under reconstruction and not from reference pictures.

There can be many different forms of intra prediction. When more thanone of such techniques can be used in a given video coding technology,the technique in use can be coded in an intra prediction mode. Incertain cases, modes can have submodes and/or parameters, and those canbe coded individually or included in the mode codeword. Which codewordto use for a given mode/submode/parameter combination can have an impactin the coding efficiency gain through intra prediction, and so can theentropy coding technology used to translate the codewords into abitstream.

A certain mode of intra prediction was introduced with H.264, refined inH.265, and further refined in newer coding technologies such as jointexploration model (JEM), versatile video coding (VVC), and benchmark set(BMS). A predictor block can be formed using neighboring sample valuesbelonging to already available samples. Sample values of neighboringsamples are copied into the predictor block according to a direction. Areference to the direction in use can be coded in the bitstream or mayitself be predicted.

Referring to FIG. 1, depicted in the lower right is a subset of ninepredictor directions known from H.265's 33 possible predictor directions(corresponding to the 33 angular modes of the 35 intra modes). The pointwhere the arrows converge (101) represents the sample being predicted.The arrows represent the direction from which the sample is beingpredicted. For example, arrow (102) indicates that sample (101) ispredicted from a sample or samples to the upper right, at a 45 degreeangle from the horizontal. Similarly, arrow (103) indicates that sample(101) is predicted from a sample or samples to the lower left of sample(101), in a 22.5 degree angle from the horizontal.

Still referring to FIG. 1, on the top left there is depicted a squareblock (104) of 4×4 samples (indicated by a dashed, boldface line). Thesquare block (104) includes 16 samples, each labelled with an “S”, itsposition in the Y dimension (e.g., row index) and its position in the Xdimension (e.g., column index). For example, sample S21 is the secondsample in the Y dimension (from the top) and the first (from the left)sample in the X dimension. Similarly, sample S44 is the fourth sample inblock (104) in both the Y and X dimensions. As the block is 4×4 samplesin size, S44 is at the bottom right. Further shown are reference samplesthat follow a similar numbering scheme. A reference sample is labelledwith an R, its Y position (e.g., row index) and X position (columnindex) relative to block (104). In both H.264 and H.265, predictionsamples neighbor the block under reconstruction; therefore no negativevalues need to be used.

Intra picture prediction can work by copying reference sample valuesfrom the neighboring samples as appropriated by the signaled predictiondirection. For example, assume the coded video bitstream includessignaling that, for this block, indicates a prediction directionconsistent with arrow (102)—that is, samples are predicted from aprediction sample or samples to the upper right, at a 45 degree anglefrom the horizontal. In that case, samples S41, S32, S23, and S14 arepredicted from the same reference sample R05. Sample S44 is thenpredicted from reference sample R08.

In certain cases, the values of multiple reference samples may becombined, for example through interpolation, in order to calculate areference sample; especially when the directions are not evenlydivisible by 45 degrees.

The number of possible directions has increased as video codingtechnology has developed. In H.264 (year 2003), nine different directioncould be represented. That increased to 33 in H.265 (year 2013), andJEM/VVC/BMS, at the time of disclosure, can support up to 65 directions.Experiments have been conducted to identify the most likely directions,and certain techniques in the entropy coding are used to represent thoselikely directions in a small number of bits, accepting a certain penaltyfor less likely directions. Further, the directions themselves cansometimes be predicted from neighboring directions used in neighboring,already decoded, blocks.

FIG. 2 shows a schematic (201) that depicts 65 intra predictiondirections according to JEM to illustrate the increasing number ofprediction directions over time.

The mapping of intra prediction directions bits in the coded videobitstream that represent the direction can be different from videocoding technology to video coding technology; and can range, forexample, from simple direct mappings of prediction direction to intraprediction mode, to codewords, to complex adaptive schemes involvingmost probable modes, and similar techniques. In all cases, however,there can be certain directions that are statistically less likely tooccur in video content than certain other directions. As the goal ofvideo compression is the reduction of redundancy, those less likelydirections will, in a well working video coding technology, berepresented by a larger number of bits than more likely directions.

SUMMARY

Aspects of the disclosure provide methods and apparatuses for videoencoding/decoding. In some examples, an apparatus for video encodingand/or decoding includes processing circuitry. The processing circuitrycan encode and/or decode coding information of a block to bereconstructed from a coded video bitstream where the coding informationcan indicate intra prediction information for the block. For the blockcoded with a directional mode, the processing circuitry can determinethe directional mode based on a nominal mode and an angular offset. Thecoding information can indicate the nominal mode and the angular offset.The processing circuitry can determine a non-separable transform for theblock based on the nominal mode, and reconstruct the block based on thedirectional mode and the non-separable transform.

In an embodiment, the processing circuitry determines a transform setmode that is associated with the nominal mode, and the transform setmode indicates a set of one or more non-separable transforms thatincludes the non-separable transform.

In an embodiment, the coding information further indicates anon-separable transform index. The processing circuitry can determinethe non-separable transform in the set of one or more non-separabletransforms based on the non-separable transform index, and reconstructthe block based on the directional mode and the non-separable transform.

In an embodiment, the non-separable transform is a non-separablesecondary transform. In an example, the non-separable secondarytransform does not apply to at least one of a PAETH mode and a recursivefiltering mode. In an example, the processing circuitry applies thenon-separable secondary transform only to first N transform coefficientsalong a scanning order used for entropy coding the first transformcoefficients of the block. In an example, the processing circuitryapplies the non-separable secondary transform only to first transformcoefficients in the block, each of the first transform coefficientshaving a coordinate (x, y) and a sum of the respective x and ycoordinates being less than a threshold value. In an example, ahorizontal transform and a vertical transform in a primary transform forthe block are included in a subset of a set of line graph transforms.

In an example, the non-separable transform is a non-separable secondarytransform. The block includes first transform coefficients obtained withthe non-separable secondary transform and second transform coefficientsobtained without the non-separable secondary transform. The processingcircuitry can entropy decode the first transform coefficients and thesecond transform coefficients separately.

In an embodiment, non-directional modes include a DC mode, a PAETH mode,a SMOOTH mode, a SMOOTH_V mode, a SMOOTH_H mode, recursive filteringmodes, and a chroma from luma (CfL) mode. The DC mode, the PAETH mode,the SMOOTH mode, the SMOOTH_V mode, and the SMOOTH_H mode can be basedon averaging of neighboring samples of the block. For the block codedwith one of the non-directional modes, the processing circuitry candetermine a set of one or more non-separable transforms associated withthe one of the non-directional modes. One of (a) at least another one ofthe non-directional modes and (b) a nominal mode can be associated withthe set of one or more non-separable transforms. The processingcircuitry can determine a non-separable transform in the set of one ormore non-separable transforms based on a non-separable transform indexindicated by the coding information. The processing circuitry canreconstruct the block based on the non-directional mode and thenon-separable transform.

In an embodiment, the one of the non-directional modes and the one ofthe at least another one of the non-directional modes and the nominalmode include one of (a) the recursive filtering modes and one of the DCmode and the SMOOTH mode, (b) the SMOOTH mode, the SMOOTH_H mode, andthe SMOOTH_V mode, (c) the SMOOTH mode, the SMOOTH_H mode, the SMOOTH_Vmode, and the PAETH mode, (d) the recursive filtering modes, the SMOOTHmode, and the PAETH mode, (e) a vertical mode for the nominal mode thenominal mode being a vertical mode and the SMOOTH_V mode, (f) ahorizontal mode for the nominal mode being a horizontal mode and theSMOOTH_H mode, and (v) the CfL mode and one of the DC mode, the SMOOTHmode, and the PAETH mode.

Aspects of the disclosure also provide a non-transitorycomputer-readable medium storing instructions which when executed by acomputer for video encoding and/or decoding cause the computer toperform the methods for video encoding and/or decoding.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, the nature, and various advantages of the disclosedsubject matter will be more apparent from the following detaileddescription and the accompanying drawings in which:

FIG. 1 is a schematic illustration of an exemplary subset of intraprediction modes.

FIG. 2 is an illustration of exemplary intra prediction directions.

FIG. 3 is a schematic illustration of a simplified block diagram of acommunication system (300) in accordance with an embodiment.

FIG. 4 is a schematic illustration of a simplified block diagram of acommunication system (400) in accordance with an embodiment.

FIG. 5 is a schematic illustration of a simplified block diagram of adecoder in accordance with an embodiment.

FIG. 6 is a schematic illustration of a simplified block diagram of anencoder in accordance with an embodiment.

FIG. 7 shows a block diagram of an encoder in accordance with anotherembodiment.

FIG. 8 shows a block diagram of a decoder in accordance with anotherembodiment.

FIG. 9 shows an example of nominal modes for a coding block according toan embodiment of the disclosure.

FIG. 10 shows examples for non-directional smooth intra prediction modesaccording to aspects of the disclosure.

FIG. 11 shows an example of a recursive-filtering-based intra predictoraccording to an embodiment of the disclosure.

FIG. 12 shows an example of multi-line intra prediction for a codingblock according to an embodiment of the disclosure.

FIGS. 13-14 show two exemplary transform coding processes according toembodiments of the disclosure.

FIG. 15A shows an example of a line graph transform according to anembodiment of the disclosure.

FIG. 15B shows an exemplary generalized graph Laplacian matrix accordingto an embodiment of the disclosure.

FIG. 16 shows a flow chart outlining a process (1600) according to anembodiment of the disclosure.

FIG. 17 is a schematic illustration of a computer system in accordancewith an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 3 illustrates a simplified block diagram of a communication system(300) according to an embodiment of the present disclosure. Thecommunication system (300) includes a plurality of terminal devices thatcan communicate with each other, via, for example, a network (350). Forexample, the communication system (300) includes a first pair ofterminal devices (310) and (320) interconnected via the network (350).In the FIG. 3 example, the first pair of terminal devices (310) and(320) performs unidirectional transmission of data. For example, theterminal device (310) may code video data (e.g., a stream of videopictures that are captured by the terminal device (310)) fortransmission to the other terminal device (320) via the network (350).The encoded video data can be transmitted in the form of one or morecoded video bitstreams. The terminal device (320) may receive the codedvideo data from the network (350), decode the coded video data torecover the video pictures and display video pictures according to therecovered video data. Unidirectional data transmission may be common inmedia serving applications and the like.

In another example, the communication system (300) includes a secondpair of terminal devices (330) and (340) that performs bidirectionaltransmission of coded video data that may occur, for example, duringvideoconferencing. For bidirectional transmission of data, in anexample, each terminal device of the terminal devices (330) and (340)may code video data (e.g., a stream of video pictures that are capturedby the terminal device) for transmission to the other terminal device ofthe terminal devices (330) and (340) via the network (350). Eachterminal device of the terminal devices (330) and (340) also may receivethe coded video data transmitted by the other terminal device of theterminal devices (330) and (340), and may decode the coded video data torecover the video pictures and may display video pictures at anaccessible display device according to the recovered video data.

In the FIG. 3 example, the terminal devices (310), (320), (330) and(340) may be illustrated as servers, personal computers and smart phonesbut the principles of the present disclosure may be not so limited.Embodiments of the present disclosure find application with laptopcomputers, tablet computers, media players and/or dedicated videoconferencing equipment. The network (350) represents any number ofnetworks that convey coded video data among the terminal devices (310),(320), (330) and (340), including for example wireline (wired) and/orwireless communication networks. The communication network (350) mayexchange data in circuit-switched and/or packet-switched channels.Representative networks include telecommunications networks, local areanetworks, wide area networks and/or the Internet. For the purposes ofthe present discussion, the architecture and topology of the network(350) may be immaterial to the operation of the present disclosureunless explained herein below.

FIG. 4 illustrates, as an example for an application for the disclosedsubject matter, the placement of a video encoder and a video decoder ina streaming environment. The disclosed subject matter can be equallyapplicable to other video enabled applications, including, for example,video conferencing, digital TV, storing of compressed video on digitalmedia including CD, DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem (413), that caninclude a video source (401), for example a digital camera, creating forexample a stream of video pictures (402) that are uncompressed. In anexample, the stream of video pictures (402) includes samples that aretaken by the digital camera. The stream of video pictures (402),depicted as a bold line to emphasize a high data volume when compared toencoded video data (404) (or coded video bitstreams), can be processedby an electronic device (420) that includes a video encoder (403)coupled to the video source (401). The video encoder (403) can includehardware, software, or a combination thereof to enable or implementaspects of the disclosed subject matter as described in more detailbelow. The encoded video data (404) (or encoded video bitstream (404)),depicted as a thin line to emphasize the lower data volume when comparedto the stream of video pictures (402), can be stored on a streamingserver (405) for future use. One or more streaming client subsystems,such as client subsystems (406) and (408) in FIG. 4 can access thestreaming server (405) to retrieve copies (407) and (409) of the encodedvideo data (404). A client subsystem (406) can include a video decoder(410), for example, in an electronic device (430). The video decoder(410) decodes the incoming copy (407) of the encoded video data andcreates an outgoing stream of video pictures (411) that can be renderedon a display (412) (e.g., display screen) or other rendering device (notdepicted). In some streaming systems, the encoded video data (404),(407), and (409) (e.g., video bitstreams) can be encoded according tocertain video coding/compression standards. Examples of those standardsinclude ITU-T Recommendation H.265. In an example, a video codingstandard under development is informally known as Versatile Video Coding(VVC). The disclosed subject matter may be used in the context of VVC.

It is noted that the electronic devices (420) and (430) can includeother components (not shown). For example, the electronic device (420)can include a video decoder (not shown) and the electronic device (430)can include a video encoder (not shown) as well.

FIG. 5 shows a block diagram of a video decoder (510) according to anembodiment of the present disclosure. The video decoder (510) can beincluded in an electronic device (530). The electronic device (530) caninclude a receiver (531) (e.g., receiving circuitry). The video decoder(510) can be used in the place of the video decoder (410) in the FIG. 4example.

The receiver (531) may receive one or more coded video sequences to bedecoded by the video decoder (510); in the same or another embodiment,one coded video sequence at a time, where the decoding of each codedvideo sequence is independent from other coded video sequences. Thecoded video sequence may be received from a channel (501), which may bea hardware/software link to a storage device which stores the encodedvideo data. The receiver (531) may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver (531) may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory (515) may be coupled inbetween the receiver (531) and an entropy decoder/parser (520) (“parser(520)” henceforth). In certain applications, the buffer memory (515) ispart of the video decoder (510). In others, it can be outside of thevideo decoder (510) (not depicted). In still others, there can be abuffer memory (not depicted) outside of the video decoder (510), forexample to combat network jitter, and in addition another buffer memory(515) inside the video decoder (510), for example to handle playouttiming. When the receiver (531) is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosynchronous network, the buffer memory (515) may not be needed, orcan be small. For use on best effort packet networks such as theInternet, the buffer memory (515) may be required, can be comparativelylarge and can be advantageously of adaptive size, and may at leastpartially be implemented in an operating system or similar elements (notdepicted) outside of the video decoder (510).

The video decoder (510) may include the parser (520) to reconstructsymbols (521) from the coded video sequence. Categories of those symbolsinclude information used to manage operation of the video decoder (510),and potentially information to control a rendering device such as arender device (512) (e.g., a display screen) that is not an integralpart of the electronic device (530) but can be coupled to the electronicdevice (530), as was shown in FIG. 5. The control information for therendering device(s) may be in the form of Supplemental EnhancementInformation (SEI messages) or Video Usability Information (VUI)parameter set fragments (not depicted). The parser (520) mayparse/entropy-decode the coded video sequence that is received. Thecoding of the coded video sequence can be in accordance with a videocoding technology or standard, and can follow various principles,including variable length coding, Huffman coding, arithmetic coding withor without context sensitivity, and so forth. The parser (520) mayextract from the coded video sequence, a set of subgroup parameters forat least one of the subgroups of pixels in the video decoder, based uponat least one parameter corresponding to the group. Subgroups can includeGroups of Pictures (GOPs), pictures, tiles, slices, macroblocks, CodingUnits (CUs), blocks, Transform Units (TUs), Prediction Units (PUs) andso forth. The parser (520) may also extract from the coded videosequence information such as transform coefficients, quantizer parametervalues, motion vectors, and so forth.

The parser (520) may perform an entropy decoding/parsing operation onthe video sequence received from the buffer memory (515), so as tocreate symbols (521).

Reconstruction of the symbols (521) can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser (520). The flow of such subgroup control information between theparser (520) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, the video decoder (510)can be conceptually subdivided into a number of functional units asdescribed below. In a practical implementation operating undercommercial constraints, many of these units interact closely with eachother and can, at least partly, be integrated into each other. However,for the purpose of describing the disclosed subject matter, theconceptual subdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (551). Thescaler/inverse transform unit (551) receives a quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) (521) from the parser (520). The scaler/inversetransform unit (551) can output blocks comprising sample values, thatcan be input into aggregator (555).

In some cases, the output samples of the scaler/inverse transform (551)can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit (552). In some cases, the intra pictureprediction unit (552) generates a block of the same size and shape ofthe block under reconstruction, using surrounding already reconstructedinformation fetched from the current picture buffer (558). The currentpicture buffer (558) buffers, for example, partly reconstructed currentpicture and/or fully reconstructed current picture. The aggregator(555), in some cases, adds, on a per sample basis, the predictioninformation the intra prediction unit (552) has generated to the outputsample information as provided by the scaler/inverse transform unit(551).

In other cases, the output samples of the scaler/inverse transform unit(551) can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a motion compensation prediction unit (553) canaccess reference picture memory (557) to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols (521) pertaining to the block, these samples can beadded by the aggregator (555) to the output of the scaler/inversetransform unit (551) (in this case called the residual samples orresidual signal) so as to generate output sample information. Theaddresses within the reference picture memory (557) from where themotion compensation prediction unit (553) fetches prediction samples canbe controlled by motion vectors, available to the motion compensationprediction unit (553) in the form of symbols (521) that can have, forexample X, Y, and reference picture components. Motion compensation alsocan include interpolation of sample values as fetched from the referencepicture memory (557) when sub-sample exact motion vectors are in use,motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (555) can be subject to variousloop filtering techniques in the loop filter unit (556). Videocompression technologies can include in-loop filter technologies thatare controlled by parameters included in the coded video sequence (alsoreferred to as coded video bitstream) and made available to the loopfilter unit (556) as symbols (521) from the parser (520), but can alsobe responsive to meta-information obtained during the decoding ofprevious (in decoding order) parts of the coded picture or coded videosequence, as well as responsive to previously reconstructed andloop-filtered sample values.

The output of the loop filter unit (556) can be a sample stream that canbe output to the render device (512) as well as stored in the referencepicture memory (557) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. For example, once a codedpicture corresponding to a current picture is fully reconstructed andthe coded picture has been identified as a reference picture (by, forexample, the parser (520)), the current picture buffer (558) can becomea part of the reference picture memory (557), and a fresh currentpicture buffer can be reallocated before commencing the reconstructionof the following coded picture.

The video decoder (510) may perform decoding operations according to apredetermined video compression technology in a standard, such as ITU-TRec. H.265. The coded video sequence may conform to a syntax specifiedby the video compression technology or standard being used, in the sensethat the coded video sequence adheres to both the syntax of the videocompression technology or standard and the profiles as documented in thevideo compression technology or standard. Specifically, a profile canselect certain tools as the only tools available for use under thatprofile from all the tools available in the video compression technologyor standard. Also necessary for compliance can be that the complexity ofthe coded video sequence is within bounds as defined by the level of thevideo compression technology or standard. In some cases, levels restrictthe maximum picture size, maximum frame rate, maximum reconstructionsample rate (measured in, for example mega per second), maximumreference picture size, and so on. Limits set by levels can, in somecases, be further restricted through Hypothetical Reference Decoder(HRD) specifications and metadata for HRD buffer management signaled inthe coded video sequence.

In an embodiment, the receiver (531) may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder (510) to properly decode the data and/or to moreaccurately reconstruct the original video data. Additional data can bein the form of, for example, temporal, spatial, or signal noise ratio(SNR) enhancement layers, redundant slices, redundant pictures, forwarderror correction codes, and so on.

FIG. 6 shows a block diagram of a video encoder (603) according to anembodiment of the present disclosure. The video encoder (603) isincluded in an electronic device (620). The electronic device (620)includes a transmitter (640) (e.g., transmitting circuitry). The videoencoder (603) can be used in the place of the video encoder (403) in theFIG. 4 example.

The video encoder (603) may receive video samples from a video source(601) (that is not part of the electronic device (620) in the FIG. 6example) that may capture video image(s) to be coded by the videoencoder (603). In another example, the video source (601) is a part ofthe electronic device (620).

The video source (601) may provide the source video sequence to be codedby the video encoder (603) in the form of a digital video sample streamthat can be of any suitable bit depth (for example: 8 bit, 10 bit, 12bit, . . . ), any color_space (for example, BT.601 Y CrCB, RGB, . . . ),and any suitable sampling structure (for example Y CrCb 4:2:0, Y CrCb4:4:4). In a media serving system, the video source (601) may be astorage device storing previously prepared video. In a videoconferencingsystem, the video source (601) may be a camera that captures local imageinformation as a video sequence. Video data may be provided as aplurality of individual pictures that impart motion when viewed insequence. The pictures themselves may be organized as a spatial array ofpixels, wherein each pixel can comprise one or more samples depending onthe sampling structure, color space, etc. in use. A person skilled inthe art can readily understand the relationship between pixels andsamples. The description below focuses on samples.

According to an embodiment, the video encoder (603) may code andcompress the pictures of the source video sequence into a coded videosequence (643) in real time or under any other time constraints asrequired by the application. Enforcing appropriate coding speed is onefunction of a controller (650). In some embodiments, the controller(650) controls other functional units as described below and isfunctionally coupled to the other functional units. The coupling is notdepicted for clarity. Parameters set by the controller (650) can includerate control related parameters (picture skip, quantizer, lambda valueof rate-distortion optimization techniques, . . . ), picture size, groupof pictures (GOP) layout, maximum motion vector search range, and soforth. The controller (650) can be configured to have other suitablefunctions that pertain to the video encoder (603) optimized for acertain system design.

In some embodiments, the video encoder (603) is configured to operate ina coding loop. As an oversimplified description, in an example, thecoding loop can include a source coder (630) (e.g., responsible forcreating symbols, such as a symbol stream, based on an input picture tobe coded, and a reference picture(s)), and a (local) decoder (633)embedded in the video encoder (603). The decoder (633) reconstructs thesymbols to create the sample data in a similar manner as a (remote)decoder also would create (as any compression between symbols and codedvideo bitstream is lossless in the video compression technologiesconsidered in the disclosed subject matter). The reconstructed samplestream (sample data) is input to the reference picture memory (634). Asthe decoding of a symbol stream leads to bit-exact results independentof decoder location (local or remote), the content in the referencepicture memory (634) is also bit exact between the local encoder andremote encoder. In other words, the prediction part of an encoder “sees”as reference picture samples exactly the same sample values as a decoderwould “see” when using prediction during decoding. This fundamentalprinciple of reference picture synchronicity (and resulting drift, ifsynchronicity cannot be maintained, for example because of channelerrors) is used in some related arts as well.

The operation of the “local” decoder (633) can be the same as of a“remote” decoder, such as the video decoder (510), which has alreadybeen described in detail above in conjunction with FIG. 5. Brieflyreferring also to FIG. 5, however, as symbols are available andencoding/decoding of symbols to a coded video sequence by an entropycoder (645) and the parser (520) can be lossless, the entropy decodingparts of the video decoder (510), including the buffer memory (515), andparser (520) may not be fully implemented in the local decoder (633).

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. For this reason, thedisclosed subject matter focuses on decoder operation. The descriptionof encoder technologies can be abbreviated as they are the inverse ofthe comprehensively described decoder technologies. Only in certainareas a more detail description is required and provided below.

During operation, in some examples, the source coder (630) may performmotion compensated predictive coding, which codes an input picturepredictively with reference to one or more previously coded picture fromthe video sequence that were designated as “reference pictures.” In thismanner, the coding engine (632) codes differences between pixel blocksof an input picture and pixel blocks of reference picture(s) that may beselected as prediction reference(s) to the input picture.

The local video decoder (633) may decode coded video data of picturesthat may be designated as reference pictures, based on symbols createdby the source coder (630). Operations of the coding engine (632) mayadvantageously be lossy processes. When the coded video data may bedecoded at a video decoder (not shown in FIG. 6), the reconstructedvideo sequence typically may be a replica of the source video sequencewith some errors. The local video decoder (633) replicates decodingprocesses that may be performed by the video decoder on referencepictures and may cause reconstructed reference pictures to be stored inthe reference picture cache (634). In this manner, the video encoder(603) may store copies of reconstructed reference pictures locally thathave common content as the reconstructed reference pictures that will beobtained by a far-end video decoder (absent transmission errors).

The predictor (635) may perform prediction searches for the codingengine (632). That is, for a new picture to be coded, the predictor(635) may search the reference picture memory (634) for sample data (ascandidate reference pixel blocks) or certain metadata such as referencepicture motion vectors, block shapes, and so on, that may serve as anappropriate prediction reference for the new pictures. The predictor(635) may operate on a sample block-by-pixel block basis to findappropriate prediction references. In some cases, as determined bysearch results obtained by the predictor (635), an input picture mayhave prediction references drawn from multiple reference pictures storedin the reference picture memory (634).

The controller (650) may manage coding operations of the source coder(630), including, for example, setting of parameters and subgroupparameters used for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder (645). The entropy coder (645)translates the symbols as generated by the various functional units intoa coded video sequence, by lossless compressing the symbols according totechnologies such as Huffman coding, variable length coding, arithmeticcoding, and so forth.

The transmitter (640) may buffer the coded video sequence(s) as createdby the entropy coder (645) to prepare for transmission via acommunication channel (660), which may be a hardware/software link to astorage device which would store the encoded video data. The transmitter(640) may merge coded video data from the video coder (603) with otherdata to be transmitted, for example, coded audio data and/or ancillarydata streams (sources not shown).

The controller (650) may manage operation of the video encoder (603).During coding, the controller (650) may assign to each coded picture acertain coded picture type, which may affect the coding techniques thatmay be applied to the respective picture. For example, pictures oftenmay be assigned as one of the following picture types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other picture in the sequence as a source ofprediction. Some video codecs allow for different types of intrapictures, including, for example Independent Decoder Refresh (“IDR”)Pictures. A person skilled in the art is aware of those variants of Ipictures and their respective applications and features.

A predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A bi-directionally predictive picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredictively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predictively or they may be coded predictively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded predictively, viaspatial prediction or via temporal prediction with reference to onepreviously coded reference picture. Blocks of B pictures may be codedpredictively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video encoder (603) may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video encoder (603) may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter (640) may transmit additional datawith the encoded video. The source coder (630) may include such data aspart of the coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, SEI messages, VUI parameter setfragments, and so on.

A video may be captured as a plurality of source pictures (videopictures) in a temporal sequence. Intra-picture prediction (oftenabbreviated to intra prediction) makes use of spatial correlation in agiven picture, and inter-picture prediction makes uses of the (temporalor other) correlation between the pictures. In an example, a specificpicture under encoding/decoding, which is referred to as a currentpicture, is partitioned into blocks. When a block in the current pictureis similar to a reference block in a previously coded and still bufferedreference picture in the video, the block in the current picture can becoded by a vector that is referred to as a motion vector. The motionvector points to the reference block in the reference picture, and canhave a third dimension identifying the reference picture, in casemultiple reference pictures are in use.

In some embodiments, a bi-prediction technique can be used in theinter-picture prediction. According to the bi-prediction technique, tworeference pictures, such as a first reference picture and a secondreference picture that are both prior in decoding order to the currentpicture in the video (but may be in the past and future, respectively,in display order) are used. A block in the current picture can be codedby a first motion vector that points to a first reference block in thefirst reference picture, and a second motion vector that points to asecond reference block in the second reference picture. The block can bepredicted by a combination of the first reference block and the secondreference block.

Further, a merge mode technique can be used in the inter-pictureprediction to improve coding efficiency.

According to some embodiments of the disclosure, predictions, such asinter-picture predictions and intra-picture predictions are performed inthe unit of blocks. For example, according to the HEVC standard, apicture in a sequence of video pictures is partitioned into coding treeunits (CTU) for compression, the CTUs in a picture have the same size,such as 64×64 pixels, 32×32 pixels, or 16×16 pixels. In general, a CTUincludes three coding tree blocks (CTBs), which are one luma CTB and twochroma CTBs. Each CTU can be recursively quadtree split into one ormultiple coding units (CUs). For example, a CTU of 64×64 pixels can besplit into one CU of 64×64 pixels, or 4 CUs of 32×32 pixels, or 16 CUsof 16×16 pixels. In an example, each CU is analyzed to determine aprediction type for the CU, such as an inter prediction type or an intraprediction type. The CU is split into one or more prediction units (PUs)depending on the temporal and/or spatial predictability. Generally, eachPU includes a luma prediction block (PB), and two chroma PBs. In anembodiment, a prediction operation in coding (encoding/decoding) isperformed in the unit of a prediction block. Using a luma predictionblock as an example of a prediction block, the prediction block includesa matrix of values (e.g., luma values) for pixels, such as 8×8 pixels,16×16 pixels, 8×16 pixels, 16×8 pixels, and the like.

FIG. 7 shows a diagram of a video encoder (703) according to anotherembodiment of the disclosure. The video encoder (703) is configured toreceive a processing block (e.g., a prediction block) of sample valueswithin a current video picture in a sequence of video pictures, andencode the processing block into a coded picture that is part of a codedvideo sequence. In an example, the video encoder (703) is used in theplace of the video encoder (403) in the FIG. 4 example.

In an HEVC example, the video encoder (703) receives a matrix of samplevalues for a processing block, such as a prediction block of 8×8samples, and the like. The video encoder (703) determines whether theprocessing block is best coded using intra mode, inter mode, orbi-prediction mode using, for example, rate-distortion optimization.When the processing block is to be coded in intra mode, the videoencoder (703) may use an intra prediction technique to encode theprocessing block into the coded picture; and when the processing blockis to be coded in inter mode or bi-prediction mode, the video encoder(703) may use an inter prediction or bi-prediction technique,respectively, to encode the processing block into the coded picture. Incertain video coding technologies, merge mode can be an inter pictureprediction submode where the motion vector is derived from one or moremotion vector predictors without the benefit of a coded motion vectorcomponent outside the predictors. In certain other video codingtechnologies, a motion vector component applicable to the subject blockmay be present. In an example, the video encoder (703) includes othercomponents, such as a mode decision module (not shown) to determine themode of the processing blocks.

In the FIG. 7 example, the video encoder (703) includes the interencoder (730), an intra encoder (722), a residue calculator (723), aswitch (726), a residue encoder (724), a general controller (721), andan entropy encoder (725) coupled together as shown in FIG. 7.

The inter encoder (730) is configured to receive the samples of thecurrent block (e.g., a processing block), compare the block to one ormore reference blocks in reference pictures (e.g., blocks in previouspictures and later pictures), generate inter prediction information(e.g., description of redundant information according to inter encodingtechnique, motion vectors, merge mode information), and calculate interprediction results (e.g., predicted block) based on the inter predictioninformation using any suitable technique. In some examples, thereference pictures are decoded reference pictures that are decoded basedon the encoded video information.

The intra encoder (722) is configured to receive the samples of thecurrent block (e.g., a processing block), in some cases compare theblock to blocks already coded in the same picture, generate quantizedcoefficients after transform, and in some cases also intra predictioninformation (e.g., an intra prediction direction information accordingto one or more intra encoding techniques). In an example, the intraencoder (722) also calculates intra prediction results (e.g., predictedblock) based on the intra prediction information and reference blocks inthe same picture.

The general controller (721) is configured to determine general controldata and control other components of the video encoder (703) based onthe general control data. In an example, the general controller (721)determines the mode of the block, and provides a control signal to theswitch (726) based on the mode. For example, when the mode is the intramode, the general controller (721) controls the switch (726) to selectthe intra mode result for use by the residue calculator (723), andcontrols the entropy encoder (725) to select the intra predictioninformation and include the intra prediction information in thebitstream; and when the mode is the inter mode, the general controller(721) controls the switch (726) to select the inter prediction resultfor use by the residue calculator (723), and controls the entropyencoder (725) to select the inter prediction information and include theinter prediction information in the bitstream.

The residue calculator (723) is configured to calculate a difference(residue data) between the received block and prediction resultsselected from the intra encoder (722) or the inter encoder (730). Theresidue encoder (724) is configured to operate based on the residue datato encode the residue data to generate the transform coefficients. In anexample, the residue encoder (724) is configured to convert the residuedata from a spatial domain to a frequency domain, and generate thetransform coefficients. The transform coefficients are then subject toquantization processing to obtain quantized transform coefficients. Invarious embodiments, the video encoder (703) also includes a residuedecoder (728). The residue decoder (728) is configured to performinverse-transform, and generate the decoded residue data. The decodedresidue data can be suitably used by the intra encoder (722) and theinter encoder (730). For example, the inter encoder (730) can generatedecoded blocks based on the decoded residue data and inter predictioninformation, and the intra encoder (722) can generate decoded blocksbased on the decoded residue data and the intra prediction information.The decoded blocks are suitably processed to generate decoded picturesand the decoded pictures can be buffered in a memory circuit (not shown)and used as reference pictures in some examples.

The entropy encoder (725) is configured to format the bitstream toinclude the encoded block. The entropy encoder (725) is configured toinclude various information according to a suitable standard, such asthe HEVC standard. In an example, the entropy encoder (725) isconfigured to include the general control data, the selected predictioninformation (e.g., intra prediction information or inter predictioninformation), the residue information, and other suitable information inthe bitstream. Note that, according to the disclosed subject matter,when coding a block in the merge submode of either inter mode orbi-prediction mode, there is no residue information.

FIG. 8 shows a diagram of a video decoder (810) according to anotherembodiment of the disclosure. The video decoder (810) is configured toreceive coded pictures that are part of a coded video sequence, anddecode the coded pictures to generate reconstructed pictures. In anexample, the video decoder (810) is used in the place of the videodecoder (410) in the FIG. 4 example.

In the FIG. 8 example, the video decoder (810) includes an entropydecoder (871), an inter decoder (880), a residue decoder (873), areconstruction module (874), and an intra decoder (872) coupled togetheras shown in FIG. 8.

The entropy decoder (871) can be configured to reconstruct, from thecoded picture, certain symbols that represent the syntax elements ofwhich the coded picture is made up. Such symbols can include, forexample, the mode in which a block is coded (such as, for example, intramode, inter mode, bi-predicted mode, the latter two in merge submode oranother submode), prediction information (such as, for example, intraprediction information or inter prediction information) that canidentify certain sample or metadata that is used for prediction by theintra decoder (872) or the inter decoder (880), respectively, residualinformation in the form of, for example, quantized transformcoefficients, and the like. In an example, when the prediction mode isinter or bi-predicted mode, the inter prediction information is providedto the inter decoder (880); and when the prediction type is the intraprediction type, the intra prediction information is provided to theintra decoder (872). The residual information can be subject to inversequantization and is provided to the residue decoder (873).

The inter decoder (880) is configured to receive the inter predictioninformation, and generate inter prediction results based on the interprediction information.

The intra decoder (872) is configured to receive the intra predictioninformation, and generate prediction results based on the intraprediction information.

The residue decoder (873) is configured to perform inverse quantizationto extract de-quantized transform coefficients, and process thede-quantized transform coefficients to convert the residual from thefrequency domain to the spatial domain. The residue decoder (873) mayalso require certain control information (to include the QuantizerParameter (QP)), and that information may be provided by the entropydecoder (871) (data path not depicted as this may be low volume controlinformation only).

The reconstruction module (874) is configured to combine, in the spatialdomain, the residual as output by the residue decoder (873) and theprediction results (as output by the inter or intra prediction modulesas the case may be) to form a reconstructed block, that may be part ofthe reconstructed picture, which in turn may be part of thereconstructed video. It is noted that other suitable operations, such asa deblocking operation and the like, can be performed to improve thevisual quality.

It is noted that the video encoders (403), (603), and (703), and thevideo decoders (410), (510), and (810) can be implemented using anysuitable technique. In an embodiment, the video encoders (403), (603),and (703), and the video decoders (410), (510), and (810) can beimplemented using one or more integrated circuits. In anotherembodiment, the video encoders (403), (603), and (603), and the videodecoders (410), (510), and (810) can be implemented using one or moreprocessors that execute software instructions.

Video coding technologies related to a non-separable transform, forexample, used in a primary transform and/or a secondary transform, forintra coding are disclosed. The non-separable transform can beapplicable in any suitable video coding format or standard. The videocoding format can include an open video coding format designed for videotransmissions over the Internet, such as AOMedia Video 1 (AV1) or a nextgeneration AOMedia Video format beyond the AV1. The video codingstandard can include High Efficiency Video Coding (HEVC) standard, anext-generation video coding beyond HEVC (e.g., the Versatile VideoCoding (VVC)), or the like.

Various intra prediction modes can be used in intra prediction, forexample, in AV1, VVC, and/or the like. In an embodiment, such as in theAV1, directional intra prediction is used. In an example, such as in anopen video coding format VP9, eight directional modes corresponding toeight angles from 45° to 207°. To exploit more varieties of spatialredundancy in directional textures, for example in the AV1, directionalmodes (also referred to as directional intra modes, directional intraprediction modes, angular modes) can be extended to an angular set withfiner granularity, as shown in FIG. 9.

FIG. 9 shows an example of nominal modes for a coding block (CB) (910)according to an embodiment of the disclosure. Certain angles (referredto as nominal angles) can correspond to nominal modes. In an example,eight nominal angles (or nominal intra angles) (901)-(908) correspond toeight nominal modes (e.g., V_PRED, H_PRED, D45_PRED, D135_PRED,D113_PRED, D157_PRED, D203_PRED, and D67_PRED). The eight nominal angles(901)-(908) as well as the eight nominal modes can be referred to asV_PRED, H_PRED, D45_PRED, D135_PRED, D113_PRED, D157_PRED, D203_PRED,and D67_PRED, respectively. Further, each nominal angle can correspondto a plurality of finer angles (e.g., seven finer angles), and thus 56angles (or prediction angles) or 56 directional modes (or angular modes,directional intra prediction modes) can be used, for example, in theAV1. Each prediction angle can be presented by a nominal angle and anangular offset (or an angle delta). The angular offset can be obtainedby multiplying an offset integer I (e.g., −3, −2, −1, 0, 1, 2, or 3)with a step size (e.g., 3°). In an example, the prediction angle isequal to a sum of the nominal angle and the angular offset. In anexample, such as in the AV1, the nominal modes (e.g., the eight nominalmodes (901)-(908)) together with certain non-angular smooth modes (e.g.,a DC mode, a PAETH mode, a SMOOTH mode, a vertical SMOOTH mode, and ahorizontal SMOOTH mode as described below) can be signaled.Subsequently, if a current prediction mode is a directional mode (or anangular mode), an index can be further signaled to indicate the angularoffset (e.g., the offset integer I) corresponding to the nominal angle.In an example, to implement directional prediction modes via a genericway, the 56 directional modes such as used in the AV1 are implementedwith a unified directional predictor that can project each pixel to areference sub-pixel location and interpolate the reference pixel by a2-tap bilinear filter.

Non-directional smooth intra predictors (also referred to asnon-directional smooth intra prediction modes, non-directional smoothmodes, non-angular smooth modes) can be used in intra prediction for aCB. In some examples (e.g., in the AV1), five non-directional smoothintra prediction modes include the DC mode or the DC predictor (e.g.,DC), the PAETH mode or the PAETH predictor (e.g., PAETH), the SMOOTHmode or the SMOOTH predictor (e.g., SMOOTH), the vertical SMOOTH mode(referred to as the SMOOTH_V mode, the SMOOTH_V predictor, theSMOOTH_V), and the horizontal SMOOTH mode (referred to as the SMOOTH_Hmode, the SMOOTH_H predictor, or SMOOTH_H).

FIG. 10 shows examples for non-directional smooth intra prediction modes(e.g., the DC mode, the PAETH mode, the SMOOTH mode, the SMOOTH_V mode,and the SMOOTH_H mode) according to aspects of the disclosure. Topredict a sample (1001) in a CB (1000) based on the DC predictor, anaverage of a first value of a left neighboring sample (1012) and asecond value of an above neighboring sample (or a top neighboringsample) (1011) can be used as a predictor.

To predict the sample (1001) based on the PAETH predictor, the firstvalue of the left neighboring sample (1012), the second value of the topneighboring sample (1011), and a third value for a top-left neighboringsample (1013) can be obtained. Then, a reference value is obtained usingEq. 1.

reference value=first value+second value−third value  (Eq. 1)

One of the first value, the second value, and the third value that isclosest to the reference value can be set as the predictor for thesample (1001).

The SMOOTH_V mode, the SMOOTH_H mode, and the SMOOTH mode can predictthe CB (1000) using a quadratic interpolation in a vertical direction, ahorizontal direction, and an average of the vertical direction and thehorizontal direction, respectively. To predict the sample (1001) basedon the SMOOTH predictor, an average (e.g., a weighted combination) ofthe first value, the second value, a value of a right sample (1014), anda value of a bottom sample (1016) can be used. In various examples, theright sample (1014) and the bottom sample (1016) are not reconstructed,and thus, a value of a top-right neighboring sample (1015) and a valueof a bottom-left neighboring sample (1017) can replace the values of theright sample (1014) and the bottom sample (1016), respectively.Accordingly, an average (e.g., a weighted combination) of the firstvalue, the second value, the value of the top-right neighboring sample(1015), and the value of the bottom-left neighboring sample (1017) canbe used as the SMOOTH predictor. To predict the sample (1001) based onthe SMOOTH_V predictor, an average (e.g., a weighted combination) of thesecond value of the top neighboring sample (1011) and the value of thebottom-left neighboring sample (1017) can be used. To predict the sample(1001) based on the SMOOTH_H predictor, an average (e.g., a weightedcombination) of the first value of the left neighboring sample (1012)and the value of the top-right neighboring sample (1015) can be used.

FIG. 11 shows an example of a recursive-filtering-based intra predictor(also referred to as a filter intra mode, or a recursive filtering mode)according to an embodiment of the disclosure. To capture a decayingspatial correlation with references on the edges, a filter intra modecan be used for a CB (1100). In an example, the CB (1100) is a lumablock. The luma block (1100) can be divided into multiple patches (e.g.,eight 4×2 patches B0-B7). Each of the patches B0-B7 can have a pluralityof neighboring samples. For example, the patch B0 has seven neighboringsamples (or seven neighbors) R00-R06 including four top neighboringsamples R01-R04, two left neighboring samples R05-R06, and a top-leftneighboring sample R00. Similarly, the patch B7 has seven neighboringsamples R70-R76 including four top neighboring samples R71-R74, two leftneighboring samples R75-R76, and a top-left neighboring sample R70.

In some examples, multiple (e.g., five) filter intra modes (or multiplerecursive filtering modes) are pre-designed, for example, for the AV1.Each filter intra mode can be represented by a set of eight 7-tapfilters reflecting correlation between samples (or pixels) in acorresponding 4×2 patch (e.g., B0) and seven neighbors (e.g., R00-R06)that are adjacent to the 4×2 patch B0. Weighting factors for the 7-tapfilter can be position dependent. For each of the patches B0-B7, theseven neighbors (e.g., R00-R06 for B0, R70-R76 for B7) can be used topredict the samples in the corresponding patch. In an example, theneighbors R00-R06 are used to predict the samples in the patch B0. In anexample, the neighbors R70-R76 are used to predict the samples in thepatch B7. For certain patches in the CB (1100), such as the patch B0,all the seven neighbors (e.g., R00-R06) are already reconstructed. Forother patches in the CB (1100), at least one of the seven neighbors isnot reconstructed, and thus predicted value(s) of immediate neighbor(s)(or prediction sample(s) of immediate neighbor(s)) can be used asreference(s). For example, the seven neighbors R70-R76 of the patch B7are not reconstructed, so the prediction samples of the immediateneighbors can be used.

A chroma sample can be predicted from a luma sample. In an embodiment, achroma from luma mode (e.g., a CfL mode, a CfL predictor) is achroma-only intra predictor that can model chroma samples (or pixels) asa linear function of coincident reconstructed luma samples (or pixels).For example, the CfL prediction can be expressed using Eq. 2 as below.

CfL(α)=αL ^(A) +D  (Eq. 2)

where L^(A) denotes an AC contribution of a luma component, a denotes ascaling parameter of the linear model, and D denotes a DC contributionof a chroma component. In an example, reconstructed luma pixels aresubsampled based on a chroma resolution, and an average value issubtracted to form the AC contribution (e.g., L^(A)). To approximate achroma AC component from the AC contribution, instead of requiring adecoder to calculate the scaling parameter α, in some examples, such asin the AV1, the CfL mode determines the scaling parameter α based onoriginal chroma pixels and signals the scaling parameter α in abitstream, and thus reducing decoder complexity and yielding a moreprecise prediction. The DC contribution of the chroma component can becomputed using an intra DC mode. The intra DC mode can be sufficient formost chroma content and have mature fast implementations.

Multi-line intra prediction can use more reference lines for intraprediction. A reference line can include multiple samples in a picture.In an example, the reference line includes samples in a row and samplesin a column. In an example, an encoder can determine and signal areference line used to generate the intra predictor. An index (alsoreferred to as a reference line index) indicating the reference line canbe signaled before intra prediction mode(s). In an example, only theMPMs are allowed when a nonzero reference line index is signaled. FIG.12 shows an example of four reference lines for a CB (1210). Referringto FIG. 12, a reference line can include up to six segments, e.g.,Segments A to F, and a top-left reference sample. For example, thereference line 0 includes the Segments B and E and a top-left referencesample. For example, the reference line 3 includes the Segments A to Fand a top-left reference sample. The Segment A and F can be padded withclosest samples from the Segment B and E, respectively. In someexamples, such as in the HEVC, only one reference line (e.g., thereference line 0 that is adjacent to the CB (1210)) is used for intraprediction. In some examples, such as in the VVC, multiple referencelines (e.g., the reference lines 0, 1, and 3) are used for intraprediction.

A transform, such as a primary transform, a secondary transform, can beapplied to a CB. The transform can be a non-separable transform or aseparable transform. According to aspects of the disclosure, thetransform (e.g., a primary transform, a secondary transform) can be anon-separable transform. Application of a non-separable transform can bedescribed as follows using a 4×4 input block (or an input matrix) X asan example (shown in Eq. 3). To apply the 4×4 non-separable transform,the 4×4 input block X can be represented by a vector {right arrow over(X)}, as shown in Eqs. 3-4.

$\begin{matrix}{\mspace{79mu} {X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}}} & \left( {{Eq}.\mspace{14mu} 3} \right) \\{\overset{\rightharpoonup}{X} = \left\lbrack {X_{00}X_{01}X_{02}X_{03}X_{10}X_{11}X_{12}X_{13}X_{20}X_{21}X_{22}X_{23}X_{30}X_{31}X_{32}X_{33}} \right\rbrack^{T}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

The non-separable transform can be calculated as

=T·

, where

indicates a transform coefficient vector, and T is a 16×16 transformmatrix. The 16×1 coefficient vector

can be subsequently reorganized into a 4×4 output block (or an outputmatrix, a coefficient block) using a scanning order (e.g., a horizontalscanning order, a vertical scanning order, a zigzag scanning order, or adiagonal scanning order) for the 4×4 input block. The transformcoefficients with smaller indices can be placed with smaller scanningindices in the 4×4 coefficient block.

According to aspects of the disclosure, a reduced non-separabletransform can be used in a primary transform. A reduced non-separabletransform can be used in a secondary transform, such as a low-frequencynon-separable transform (LFNST).

A non-separable secondary transform can be applied to a CB. In someexamples, such as in the VVC, the LFNST is applied between a forwardprimary transform and quantization (e.g., at an encoder side) andbetween de-quantization and an inverse primary transform (e.g., at adecoder side) as shown in FIGS. 13-14. In an example, the LFNST isreferred to as a reduced secondary transform (RST).

FIGS. 13-14 show examples of two transform coding processes (1300) and(1400) using a 16×64 transform (or a 64×16 transform depending onwhether the transform is a forward or inverse secondary transform) and a16×48 transform (or a 48×16 transform depending on whether the transformis a forward or inverse secondary transform), respectively. Referring toFIG. 13, in the process (1300), at an encoder side, a forward primarytransform (1310) can first be performed over a block (e.g., a residualblock) to obtain a coefficient block (1313). Subsequently, a forwardsecondary transform (or a forward LFNST) (1312) can be applied to thecoefficient block (1313). In the forward secondary transform (1312), 64coefficients of 4×4 sub-blocks A-D at a top-left corner of thecoefficient block (1313) can be represented by a 64-length vector, andthe 64-length vector can be multiplied with a transform matrix of 64×16(i.e., a width of 64 and a height of 16), resulting in a 16-lengthvector. Elements in the 16-length vector are filled back into thetop-left 4×4 sub-block A of the coefficient block (1313). Thecoefficients in the sub-blocks B-D can be zero. The resultingcoefficients after the forward secondary transform (1312) are thenquantized at a step (1314), and entropy-coded to generate coded bits ina bitstream (1316).

The coded bits can be received at a decoder side, and entropy-decodedfollowed by a de-quantization (1324) to generate a coefficient block(1323). An inverse secondary transform (or an inverse LFNST) (1322),such as an inverse RST8×8, can be performed to obtain 64 coefficients,for example, from the 16 coefficients at a top-left 4×4 sub-block E. The64 coefficients can be filled back to the 4×4 sub-blocks E-H. Further,the coefficients in the coefficient block (1323) after the inversesecondary transform (1322) can be processed with an inverse primarytransform (1320) to obtain a recovered residual block.

The process (1400) of the FIG. 14 example is similar to the process(1300) except that fewer (i.e., 48) coefficients are processed duringthe forward secondary transform (1412). Specifically, the 48coefficients in the sub-blocks A-C are processed with a smallertransform matrix of a size of 48×16. Using the smaller transform matrixof 48×16 can reduce a memory size for storing the transform matrix and anumber of calculations (e.g., multiplications, additions, subtractions,and/or the like), and thus can reduce computation complexity.

In an example, a 4×4 non-separable transform (e.g., a 4×4 LFNST) or an8×8 non-separable transform (e.g., an 8×8 LFNST) is applied according toa block size of the CB. The block size of the CB can include a width, aheight, or the like. For example, the 4×4 LFNST is applied for the CBwhere a minimum of the width and the height is less than a threshold,such as 8 (e.g., min (the width, the height)<8). For example, the 8×8LFNST is applied for the CB where the minimum of the width and theheight is larger than a threshold, such as 4 (e.g., min (width,height)>4).

A non-separable transform (e.g., the LFNST) can be based on a directmatrix multiplication approach, and thus can be implemented in a singlepass without iteration. To reduce a non-separable transform matrixdimension and to minimize computational complexity and memory space tostore transform coefficients, a reduced non-separable transform method(or RST) can be used in the LFNST. Accordingly, in the reducednon-separable transform, an N (e.g., N is 64 for an 8×8 non-separablesecondary transform (NSST)) dimensional vector can be mapped to an Rdimensional vector in a different space, where N/R (R<N) is a reductionfactor. Hence, instead of an N×N matrix, an RST matrix is an R×N matrixas described in Eq. 5.

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & \; & t_{2N} \\\; & \vdots & \; & \ddots & \vdots \\t_{R1} & t_{R2} & t_{R3} & \cdots & t_{RN}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 5} \right)\end{matrix}$

In Eq. 5, R rows of the R×N transform matrix are R bases of the Ndimensional space. The inverse transform matrix can be a transpose ofthe transform matrix (e.g., T_(R×N)) used in the forward transform. Foran 8×8 LFNST, a reduction factor of 4 can be applied, and a 64×64 directmatrix used in an 8×8 non-separable transform can be reduced to a 16×64direct matrix, as shown in FIG. 13. Alternatively, a reduction factorlarger than 4 can be applied, and the 64×64 direct matrix used in the8×8 non-separable transform can be reduced to a 16×48 direct matrix, asshown in FIG. 14. Hence, a 48×16 inverse RST matrix can be used at adecoder side to generate core (primary) transform coefficients in an 8×8top-left region.

Referring to FIG. 14, when the 16×48 matrix is applied instead of the16×64 matrix with a same transform set configuration, an input to the16×48 matrix includes 48 input data from three 4×4 blocks A, B, and C ina top-left 8×8 block excluding a right-bottom 4×4 block D. With areduction in the dimension, a memory usage for storing LFNST matricescan be reduced, for example, from 10 KB to 8 KB with a minimalperformance drop.

In order to reduce complexity, the LFNST can be restricted to beapplicable if coefficients outside a first coefficient subgroup arenon-significant. In an example, the LFNST can be restricted to beapplicable only if all coefficients outside the first coefficientsubgroup are non-significant. Referring to FIGS. 13-14, the firstcoefficient subgroup corresponds to the top-left block E, and thus thecoefficients that are outside the block E are non-significant.

In an example, primary-only transform coefficients are non-significant(e.g., zero) when the LFNST is applied. The primary-only transformcoefficients can refer to transform coefficients that are obtained froma primary transform without a secondary transform. Accordingly, an LFNSTindex signaling can be conditioned on a last-significant position, andthus avoiding an extra coefficient scanning in the LFNST. In someexamples, the extra coefficient scanning is used to check significanttransform coefficients at specific positions. In an example, theworst-case handling of the LFNST, for example, in terms ofmultiplications per pixel restricts the non-separable transform for a4×4 block and an 8×8 block to an 8×16 transform and an 8×48 transform,respectively. In the above cases, the last-significant scan position canbe less than 8 when the LFNST is applied. For other sizes, thelast-significant scan position can be less than 16 when the LFNST isapplied. For a CB of 4×N and N×4 and N is larger than 8, the restrictioncan imply that the LFNST is applied to a top-left 4×4 region in the CB.In an example, the restriction implies that the LFNST is applied onlyonce to the top-left 4×4 region only in the CB. In an example, all theprimary-only coefficients are non-significant (e.g., zero) when theLFNST is applied, a number of operations for the primary transform isreduced. From an encoder perspective, quantization of transformcoefficients can be significantly simplified when the LFNST transform istested. A rate-distortion optimized quantization can be done at maximumfor the first 16 coefficients, for example, in a scanning order,remaining coefficients can be set to zero.

An LFNST transform (e.g., a transform kernel or a transform matrix) canbe selected as described below. In an embodiment, multiple transformsets can be used, and one or more non-separable transform matrices (orkernels) can be included in each of the multiple transform sets in theLFNST. According to aspects of the disclosure, a transform set can beselected from the multiple transform sets, and a non-separable transformmatrix can be selected from the one or more non-separable transformmatrices in the transform set.

Table 1 shows an exemplary mapping from intra prediction modes to themultiple transform sets according to an embodiment of the disclosure.The mapping indicates a relationship between the intra prediction modesand the multiple transform sets. The relationship, such as indicated inTable 1, can be pre-defined and can be stored in an encoder and adecoder.

Referring to Table 1, the multiple transform sets include four transformsets, e.g., transform sets 0 to 3 represented by a transform set index(e.g., Tr. set index) from 0 to 3, respectively. An index (e.g., anIntraPredMode) can indicate the intra prediction mode, and the transformset index can be obtained based on the index and Table 1. Accordingly,the transform set can be determined based on the intra prediction mode.In an example, if one of three cross component linear model (CCLM) modes(e.g., INTRA_LT_CCLM, INTRA_T_CCLM or INTRA_L_CCLM) is used for a CB(e.g., 81<=IntraPredMode<=83), the transform set 0 is selected for theCB.

As described above, each transform set can include the one or morenon-separable transform matrices. One of the one or more non-separabletransform matrices can be selected by an LFNST index that is explicitlysignaled. The LFNST index can be signaled in a bitstream once perintra-coded CU (e.g., the CB), for example, after signaling transformcoefficients. In an embodiment, each transform set includes twonon-separable transform matrices (kernels), and the selectednon-separable secondary transform candidate can be one of the twonon-separable transform matrices. In some examples, the LFNST is notapplied to a CB (e.g., the CB coded with a transform skip mode or anumber of non-zero coefficients of the CB is less than a threshold). Inan example, the LFNST index is not signaled for the CB when the LFNST isnot to be applied to the CB. A default value for the LFNST index can bezero and not signaled, indicating that the LFNST is not applied to theCB.

TABLE 1 Transform set selection table IntraPredMode Tr. set indexIntraPredMode < 0 1  0 <= IntraPredMode <= 1 0  2 <= IntraPredMode <= 121 13 <= IntraPredMode <= 23 2 24 <= IntraPredMode <= 44 3 45 <=IntraPredMode <= 55 2 56 <= IntraPredMode <= 80 1 81 <= IntraPredMode <=83 0

In an embodiment, the LFNST is restricted to be applicable only if allcoefficients outside the first coefficient subgroup are non-significant,coding of the LFNST index can depend on a position of the lastsignificant coefficient. The LFNST index can be context coded. In anexample, the context coding of the LFNST index does not depend on anintra prediction mode, and only a first bin is context coded. The LFNSTcan be applied to an intra-coded CU in an intra slice or in an interslice, and for both Luma and Chroma components. If a dual tree isenabled, LFNST indices for Luma and Chroma components can be signaledseparately. For an inter slice (e.g., the dual tree is disabled), asingle LFNST index can be signaled and used for both the Luma and Chromacomponents.

Intra sub-partition (ISP) coding mode can be used. In the ISP codingmode, a luma intra-predicted block can be divided vertically orhorizontally into 2 or 4 sub-partitions depending on a block size. Insome examples, performance improvement is marginal when the RST isapplied to every feasible sub-partition. Thus, in some examples, when anISP mode is selected, the LFNST is disabled and the LFNST index (or anRST index) is not signaled. Disabling the RST or the LFNST forISP-predicted residues can reduce coding complexity. In some examples,the LFNST is disabled and the LFNST index is not signaled when amatrix-based intra predication mode (MIP) is selected.

In some example, a CU larger than 64×64 is implicitly split (TU tiling)due to a maximum transform size restriction (e.g., 64×64), an LFNSTindex search can increase data buffering by four times for a certainnumber of decode pipeline stages. Therefore, the maximum size that theLFNST is allowed can be restricted to 64×64. In an example, the LFNST isenabled with a discrete cosine transform (DCT) type 2 (DCT-2) transformonly.

Line graph transforms (LGT) can be used, for example, in transforms suchas a primary transform. In an example, LGTs include various DCTs,discrete sine transforms (DSTs), as described below. LGTs can include32-point and 64-point 1-dimensional (1D) DSTs.

Graphs are generic mathematical structures including sets of verticesand edges that can be used for modelling affinity relations betweenobjects of interest. Weighted graphs where a set of weights are assignedto edges and optionally to vertices can provide sparse representationsfor robust modeling of signals/data. LGTs can improve coding efficiencyby providing a better adaptation for diverse block statistics. SeparableLGTs can be designed and optimized by learning line graphs from data tomodel underlying row and column-wise statistics of residual signals of ablock, and associated generalized graph Laplacian (GGL) matrices can beused to derive the LGTs.

FIG. 15A shows an example of a generic LGT characterized by self-loopweights (e.g., v_(c1), v_(c2)) and edge weights w_(c) according to anembodiment of the disclosure. Given a weighted graph G (W, V), the GGLmatrix can be defined as below.

L _(c) =D−W+V  (Eq. 6)

where W can be an adjacency matrix including the non-negative edgeweights w_(c), D can be a diagonal degree matrix, and V can be adiagonal matrix denoting the self-loop weights v_(c1) and v_(c2). FIG.15B shows an example of the matrix L_(c).

The LGT can be derived by an Eigen-decomposition of the GGL matrix L_(c)as below.

L _(c) =UΦU ^(T)  (Eq. 7)

where columns of an orthogonal matrix U can be the basis vectors of theLGT, and Φ can be a diagonal eigenvalue matrix.

In various examples, certain DCTs and DSTs (e.g., DCT-2, DCT-8 andDST-7), are subsets of a set of LGTs derived from certain forms of theGGLs. The DCT-2 can be derived by setting v_(c1) to 0 (e.g., v_(c1)=0).The DST-7 can be derived by setting v_(c1) to w_(c) (e.g.,v_(c1)=w_(c)). The DCT-8 can be derived by setting v_(c2) to w_(c)(e.g.,v_(c2)=w_(c)). The DST-4 can be derived by setting v_(c1) to2w_(c)(e.g., v_(c1)=2w_(c)). The DCT-4 can be derived by setting v_(c2)to 2w_(c) (e.g., v_(c2)=2w_(c)).

In some examples, the LGTs can be implemented as matrix multiplications.A 4p LGT core can be derived by setting v_(c1) to 2w_(c) in Lc, and thusthe 4p LGT core is the DST-4. A 8p LGT core can be derived by settingv_(c1) to 1.5w_(c) in Lc. In an example, an LGT core can be derived bysetting v_(c1) to be w_(c) and v_(c2) to be 0 and the LGT core canbecome DST-7.

In some examples, such as in the AV1, transform schemes are onlyseparable, and may not be efficient for capturing certain directionaltexture patterns, such as certain edges along a 45° direction. Fordeveloping more efficient video and image coding technologies (e.g.,advanced video and image coding technologies beyond AV1 intra coding), anon-separable transform can be used to improve coding efficiency, forexample, for certain directional image patterns.

In some examples, a non-separable transform is used in the VVC. Thesecondary transform scheme (e.g., non-separable secondary transformscheme) in the VVC can rely on an intra prediction scheme. However,intra prediction schemes of the AV1 and the VVC can be different. Thus,the secondary transform scheme in the VVC may not be fully compatiblewith the AV1 intra coding scheme. Thus, to apply a secondary transformbased on the AV1, such as in a next generation AOMedia Video formatbeyond the AV1, further changes are applied, as described in thedisclosure.

Various embodiments and examples may be used separately or combined inany order. In the disclosure, an intra prediction mode used to generateprediction samples according to a prediction direction can be referredto as an angular mode (or an angular intra prediction mode) or adirectional mode (or a directional intra prediction mode), such asdescribed above with reference to FIG. 9. An intra prediction mode usedto generate prediction samples not based on a prediction direction, suchas described above with reference to FIGS. 10-11, can be referred to asa non-directional intra prediction mode (or a non-directional mode).Non-directional intra prediction modes (or non-directional modes) caninclude non-directional smooth modes (e.g., the DC mode, the PAETH mode,the SMOOTH mode, the SMOOTH_V mode, and the SMOOTH_H mode), such asdescribed in FIG. 10, the filter intra modes (or the recursive filteringmodes) such as described in FIG. 11, the CfL mode, and the like. Certainnon-directional intra prediction modes (e.g., the non-directional smoothmodes including the DC mode, the PAETH mode, the SMOOTH mode, theSMOOTH_V mode, and the SMOOTH_H mode and the filter intra modes) can bereferred to as smooth modes.

Coding information of a block (e.g., a CB) to be reconstructed can bedecoded from a coded video bitstream. The coding information canindicate intra prediction information for the block. The intraprediction information can indicate an intra prediction mode used topredict the block. Residuals for the block can be coded using anon-separable transform. The non-separable transform can be a primarytransform or a secondary transform.

In an example, the intra prediction mode is a directional mode, and theblock is coded with the directional mode. The coding information canindicate nominal mode information and angular offset information for theblock. The nominal mode information can include a first index (e.g., anominal mode index) signaled in the coded video bitstream that indicatesa nominal mode (e.g., D45_PRED) for the block. The angular offsetinformation can include a second index (e.g., an angular offset index)signaled in the coded video bitstream that indicates an angular offsetfrom a nominal angle (e.g., 45°) corresponding to the nominal mode.

According to aspects of the disclosure, the directional mode can bedetermined based on the nominal mode and the angular offset indicated bythe coding information.

The nominal angle (e.g., 45°) can be obtained based on the nominal mode(e.g., D45_PRED), such as shown in FIG. 9. For example, the second indexcan indicate an offset integer I. Thus, the angular offset can beobtained based on the offset integer I and the step size (e.g., 3°), forexample, the angular offset is equal to the offset integer I multipliedby the step size. Accordingly, a prediction angle can be obtained basedon the nominal angle and the angular offset. In an example, theprediction angle is equal to a sum of the nominal angle and the angularoffset, as described above with reference to FIG. 9. Thus, thedirectional mode (or the intra prediction mode) can be determinedaccording to the prediction angle, as described above with reference toFIG. 9.

The non-separable transform for the block can be determined based on thenominal mode. In an embodiment, a transform set mode (e.g., stMode) thatis associated with the nominal mode can be determined where thetransform set mode can indicate a set of one or more non-separabletransforms that includes the non-separable transform. The set of one ormore non-separable transforms can be referred to as the transform set.

In an example, the directional mode is mapped to the transform set modebased on a mapping relationship between a plurality of nominal modes andtransform set modes (e.g., stMode). The mapping relationship can bestored in an encoder and a decoder. The mapping relationship can be alookup table. According to aspects of the disclosure, the directionalmode is mapped to the transform set mode based on the nominal mode(e.g., indicated by the nominal mode index) associated with thedirectional mode and regardless of the angular offset associated withthe directional mode. Then, a value of the transform set mode (e.g.,stMode) can be used to identify the transform set.

As described above, the transform set can include one or morenon-separable transforms. A signaled non-separable transform index(e.g., stIdx) can be used to further identify the non-separabletransform in the transform set. The coding information can furtherinclude the non-separable transform index (e.g., stIdx) signaled in thecoded video bitstream. The non-separable transform in the transform setcan be determined based on the non-separable transform index. The blockcan be decoded based on the non-separable transform.

The block can be reconstructed based on the directional mode and thenon-separable transform.

In an example, the non-separable transform is not applied to the blockif the block is coded with a transform skip mode. For example, thenon-separable transform index (e.g., stIdx) is not signaled, and thusindicating that no non-separable transform is applied to the block.

In an embodiment, the non-separable transform is a non-separablesecondary transform. In some examples, the non-separable secondarytransform does not apply to the PAETH mode or the recursive filteringmodes. In some examples, the non-separable secondary transform isapplied only to first N transform coefficients along a scanning orderused for entropy coding the first transform coefficients of the block.For example, at an encoder side, an input of a forward secondarytransform (e.g., a forward non-separable secondary transform) is first Ntransform coefficients along a forward scanning order, and an output ofthe forward secondary transform is N modified transform coefficientsthat replace the first N transform coefficients. At a decoder side, aninput of an inverse secondary transform (e.g., an inverse non-separablesecondary transform) is first N transform coefficients (e.g., the Nmodified transform coefficients in the output of the forward secondarytransform) along the forward scanning order, and an output of theinverse secondary transform is N transform coefficients which replacethe first N transform coefficients. The scanning order, such as theforward scanning order, can be any suitable scanning order, such as azig-zag scanning order, a diagonal scanning order, or the like. In anexample, such as in the VVC, the diagonal scanning order is applied forcoefficient coding. N can be any non-negative integer, such as in arange of from 0 to 127. In an example, when N is 0, no secondarytransform is applied to the block. In an example, N is a positiveinteger.

In an embodiment, the non-separable transform is a non-separablesecondary transform. The non-separable secondary transform is appliedonly to first transform coefficients in the block. Each of the firsttransform coefficients can have a coordinate (x, y) and a sum of therespective x and y coordinates can be less than a threshold value T. Forexample, if a coordinate (x, y) associated with a respective transformcoefficient in the block satisfy a condition that a sum of therespective x and y coordinates is greater than or equal to the thresholdvalue T, the transform coefficient can be set to 0. The transformcoefficient is not included in the first transform coefficients. Thethreshold value T can be any suitable number, such as a non-negativeinteger. In an example, T is in a range from 0 to 32.

In an embodiment, the non-separable transform is applied as anon-separable secondary transform. In an example, the non-separablesecondary transform is only applied and signaled when a type of aprimary transform for the block satisfies a condition. According toaspects of the disclosure, a horizontal transform and a verticaltransform in the primary transform for the block can be included in asubset of a set of LGTs. The horizontal transform and the verticaltransform can use a same LGT or different LGTs. The subset of the set ofLGTs can be characterized by a relationship between an edge weight w_(c)and self-loop weights (e.g., v_(c1) and/or v_(c2)). For example, thesubset of the set of LGTs is characterized by certain self-loop ratios.A self-loop ratio can be a ratio based on an edge weight w_(c) and aself-loop weight (e.g., v_(c1) or v_(c2)).

In an example, the non-separable secondary transform is only appliedwhen the horizontal transform and the vertical transform of the primarytransform is DCT-2. DCT-2 can correspond to a LGT having v_(c1)=0 (e.g.,the self-loop ratio being 0).

In an example, the non-separable secondary transform is only appliedwhen the horizontal transform and the vertical transform of the primarytransform is DST-4 (or DST-7). DST-7 can correspond to a LGT havingv_(c1)=w_(c) (e.g., the self-loop ratio being 1).

In an example, the non-separable secondary transform is only appliedwhen the following condition is satisfied. The horizontal transform ofthe primary transform is DCT-2, DST-4, or DST-7, and the verticaltransform of the primary transform is DCT-2, DST-4, or DST-7. Thehorizontal transform and the vertical transform can have a same type oftransform matrix or different types of transform matrices.

In an embodiment, the non-separable transform is applied as anon-separable secondary transform. According to aspects of thedisclosure, the block can include first transform coefficients obtainedwith the non-separable secondary transform and second transformcoefficients obtained without the non-separable secondary transform. Thefirst transform coefficients and the second transform coefficients canbe entropy coded (e.g., decoded) separately. In an example, the firsttransform coefficients are entropy coded (e.g., decoded) prior toentropy coding (e.g., decoding) the second transform coefficients. In anexample, the second transform coefficients are entropy coded (e.g.,decoded) prior to entropy coding (e.g., decoding) the first transformcoefficients.

As described above, the non-directional intra prediction modes (or thenon-directional modes) can include the DC mode, the PAETH mode, theSMOOTH mode, the SMOOTH_V mode, the SMOOTH_H mode, the recursivefiltering modes, and the CfL mode. The non-directional smooth modes caninclude the DC mode, the PAETH mode, the SMOOTH mode, the SMOOTH_V mode,and the SMOOTH_H mode, as described above with reference to FIG. 10.

In an embodiment, the block is coded with one of the non-directionalmodes. Accordingly, a set of one or more non-separable transformsassociated with the one of the non-directional modes can be determinedwhere one of (a) at least another one of the non-directional modes and(b) a nominal mode one of can be associated with the set of one or morenon-separable transforms. The nominal mode can be one of the eightnominal modes (901)-(908) V_PRED, H_PRED, D45_PRED, D135_PRED,D113_PRED, D157_PRED, D203_PRED, and D67_PRED, as described in FIG. 9. Anon-separable transform in the set of one or more non-separabletransforms can be determined based on a non-separable transform indexindicated by the coding information, similarly as described above.Subsequently, the block can be reconstructed based on thenon-directional mode and the non-separable transform.

The one of the non-directional modes and the one of the at least anotherone of the non-directional modes and the nominal mode can include one of(a) the recursive filtering modes and one of the DC mode and the SMOOTHmode, (b) the SMOOTH mode, the SMOOTH_H mode, and the SMOOTH_V mode, (c)the SMOOTH mode, the SMOOTH_H mode, the SMOOTH_V mode, and the PAETHmode, (d) the recursive filtering modes, the SMOOTH mode, and the PAETHmode, (e) V_PRED (or a vertical mode for the nominal mode) and theSMOOTH_V mode, (f) H_PRED (or a horizontal mode for the nominal mode)and the SMOOTH_H mode, and (v) the CfL mode and one of the DC mode, theSMOOTH mode, and the PAETH mode.

In general, a same set of one or more non-separable transforms can beapplied to two or more modes in a mode set including a plurality ofnominal modes (e.g., the nominal modes (901)-(908)) and a plurality ofnon-directional modes (e.g., the non-directional modes described above).

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the recursivefiltering modes (or the recursive-filtering modes) and the DC mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the recursivefiltering modes (or the recursive-filtering modes) and the SMOOTH mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the SMOOTHmode, the SMOOTH_H mode, and the SMOOTH_V mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the SMOOTHmode, the SMOOTH_H mode, the SMOOTH_V mode, and the PAETH mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the recursivefiltering modes, the SMOOTH mode, and the PAETH mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the Verticalmode (V_PRED) and the SMOOTH_V mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to theHorizontal mode (H_PRED) and the SMOOTH_H prediction mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the CfL modeand the DC mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the CfL modeand the SMOOTH mode.

A same set of one or more non-separable transforms (or a same set of oneor more non-separable transform kernels) can be applied to the CfL modeand the PAETH mode.

FIG. 16 shows a flow chart outlining a process (1600) according to anembodiment of the disclosure. The process (1600) can be used in thereconstruction of a block. In various embodiments, the process (1600)are executed by processing circuitry, such as the processing circuitryin the terminal devices (310), (320), (330) and (340), the processingcircuitry that performs functions of the video encoder (403), theprocessing circuitry that performs functions of the video decoder (410),the processing circuitry that performs functions of the video decoder(510), the processing circuitry that performs functions of the videoencoder (603), and the like. In some embodiments, the process (1600) isimplemented in software instructions, thus when the processing circuitryexecutes the software instructions, the processing circuitry performsthe process (1600). The process starts at (S1601) and proceeds to(S1610).

At (S1610), coding information of the block to be reconstructed can bedecoded from a coded video bitstream. The coding information canindicate intra prediction information for the block.

At (S1620), for the block coded with a directional mode, the directionalmode can be determined based on a nominal mode and an angular offset, asdescribed above. The coding information can indicate the nominal mode(e.g., using a nominal mode index signaled in the coded video bitstream)and the angular offset (e.g., an angular offset index signaled in thecoded video bitstream).

At (S1630), for the block coded with the directional mode, anon-separable transform for the block can be determined based on thenominal mode, as described above. A set of one or more non-separabletransforms that includes the non-separable transform can be determinedbased on the nominal mode. For example, a transform set mode that isassociated with the nominal mode is determined, and the transform setmode indicates the set of one or more non-separable transforms. Further,the coding information can indicate a non-separable transform index. Thenon-separable transform in the set of one or more non-separabletransforms can be determined based on the non-separable transform index.

At (S1640), for the block coded with the directional mode, the block canbe reconstructed based on the directional mode and the non-separabletransform. In an example, the non-separable transform is a primarytransform, and the non-separable primary transform is applied to theblock. In an example, the non-separable transform is a secondarytransform, and the non-separable secondary transform is applied to theblock. The process (1600) proceeds to (S1699), and terminates.

The process (1600) can be suitably adapted to various scenarios andsteps in the process (1600) can be adjusted accordingly. One or more ofthe steps in the process (1600) can be adapted, omitted, repeated,and/or combined. Any suitable order can be used to implement the process(1600).

Each of the methods (or embodiments), an encoder, and a decoder may beimplemented by processing circuitry (e.g., one or more processors or oneor more integrated circuits). In one example, the one or more processorsexecute a program that is stored in a non-transitory computer-readablemedium.

The techniques described above, can be implemented as computer softwareusing computer-readable instructions and physically stored in one ormore computer-readable media. For example, FIG. 17 shows a computersystem (1700) suitable for implementing certain embodiments of thedisclosed subject matter.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by one or more computer central processingunits (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 17 for computer system (1700) are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments of the present disclosure. Neither should the configurationof components be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary embodiment of a computer system (1700).

Computer system (1700) may include certain human interface inputdevices. Such a human interface input device may be responsive to inputby one or more human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard (1701), mouse (1702), trackpad (1703), touchscreen (1710), data-glove (not shown), joystick (1705), microphone(1706), scanner (1707), camera (1708).

Computer system (1700) may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen (1710), data-glove (not shown), or joystick (1705), butthere can also be tactile feedback devices that do not serve as inputdevices), audio output devices (such as: speakers (1709), headphones(not depicted)), visual output devices (such as screens (1710) toinclude CRT screens, LCD screens, plasma screens, OLED screens, eachwith or without touch-screen input capability, each with or withouttactile feedback capability—some of which may be capable to output twodimensional visual output or more than three dimensional output throughmeans such as stereographic output; virtual-reality glasses (notdepicted), holographic displays and smoke tanks (not depicted)), andprinters (not depicted).

Computer system (1700) can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW(1720) with CD/DVD or the like media (1721), thumb-drive (1722),removable hard drive or solid state drive (1723), legacy magnetic mediasuch as tape and floppy disc (not depicted), specialized ROM/ASIC/PLDbased devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system (1700) can also include an interface (1754) to one ormore communication networks (1755). Networks can for example bewireless, wireline, optical. Networks can further be local, wide-area,metropolitan, vehicular and industrial, real-time, delay-tolerant, andso on. Examples of networks include local area networks such asEthernet, wireless LANs, cellular networks to include GSM, 3G, 4G, 5G,LTE and the like, TV wireline or wireless wide area digital networks toinclude cable TV, satellite TV, and terrestrial broadcast TV, vehicularand industrial to include CANBus, and so forth. Certain networkscommonly require external network interface adapters that attached tocertain general purpose data ports or peripheral buses (1749) (such as,for example USB ports of the computer system (1700)); others arecommonly integrated into the core of the computer system (1700) byattachment to a system bus as described below (for example Ethernetinterface into a PC computer system or cellular network interface into asmartphone computer system). Using any of these networks, computersystem (1700) can communicate with other entities. Such communicationcan be uni-directional, receive only (for example, broadcast TV),uni-directional send-only (for example CANbus to certain CANbusdevices), or bi-directional, for example to other computer systems usinglocal or wide area digital networks. Certain protocols and protocolstacks can be used on each of those networks and network interfaces asdescribed above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core (1740) of thecomputer system (1700).

The core (1740) can include one or more Central Processing Units (CPU)(1741), Graphics Processing Units (GPU) (1742), specialized programmableprocessing units in the form of Field Programmable Gate Areas (FPGA)(1743), hardware accelerators for certain tasks (1744), graphics adapter(1750), and so forth. These devices, along with Read-only memory (ROM)(1745), Random-access memory (1746), internal mass storage such asinternal non-user accessible hard drives, SSDs, and the like (1747), maybe connected through a system bus (1748). In some computer systems, thesystem bus (1748) can be accessible in the form of one or more physicalplugs to enable extensions by additional CPUs, GPU, and the like. Theperipheral devices can be attached either directly to the core's systembus (1748), or through a peripheral bus (1749). In an example, a display(1710) can be connected to the graphics adapter (1750). Architecturesfor a peripheral bus include PCI, USB, and the like.

CPUs (1741), GPUs (1742), FPGAs (1743), and accelerators (1744) canexecute certain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM(1745) or RAM (1746). Transitional data can be also be stored in RAM(1746), whereas permanent data can be stored for example, in theinternal mass storage (1747). Fast storage and retrieve to any of thememory devices can be enabled through the use of cache memory, that canbe closely associated with one or more CPU (1741), GPU (1742), massstorage (1747), ROM (1745), RAM (1746), and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of the present disclosure, or they can be of the kind wellknown and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture (1700), and specifically the core (1740) can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core (1740) that are of non-transitorynature, such as core-internal mass storage (1747) or ROM (1745). Thesoftware implementing various embodiments of the present disclosure canbe stored in such devices and executed by core (1740). Acomputer-readable medium can include one or more memory devices orchips, according to particular needs. The software can cause the core(1740) and specifically the processors therein (including CPU, GPU,FPGA, and the like) to execute particular processes or particular partsof particular processes described herein, including defining datastructures stored in RAM (1746) and modifying such data structuresaccording to the processes defined by the software. In addition or as analternative, the computer system can provide functionality as a resultof logic hardwired or otherwise embodied in a circuit (for example:accelerator (1744)), which can operate in place of or together withsoftware to execute particular processes or particular parts ofparticular processes described herein. Reference to software canencompass logic, and vice versa, where appropriate. Reference to acomputer-readable media can encompass a circuit (such as an integratedcircuit (IC)) storing software for execution, a circuit embodying logicfor execution, or both, where appropriate. The present disclosureencompasses any suitable combination of hardware and software.

APPENDIX A: ACRONYMS

-   JEM: joint exploration model-   VVC: versatile video coding-   BMS: benchmark set-   MV: Motion Vector-   HEVC: High Efficiency Video Coding-   SEI: Supplementary Enhancement Information-   VUI: Video Usability Information-   GOPs: Groups of Pictures-   TUs: Transform Units,-   PUs: Prediction Units-   CTUs: Coding Tree Units-   CTBs: Coding Tree Blocks-   PBs: Prediction Blocks-   HRD: Hypothetical Reference Decoder-   SNR: Signal Noise Ratio-   CPUs: Central Processing Units-   GPUs: Graphics Processing Units-   CRT: Cathode Ray Tube-   LCD: Liquid-Crystal Display-   OLED: Organic Light-Emitting Diode-   CD: Compact Disc-   DVD: Digital Video Disc-   ROM: Read-Only Memory-   RAM: Random Access Memory-   ASIC: Application-Specific Integrated Circuit-   PLD: Programmable Logic Device-   LAN: Local Area Network-   GSM: Global System for Mobile communications-   LTE: Long-Term Evolution-   CANBus: Controller Area Network Bus-   USB: Universal Serial Bus-   PCI: Peripheral Component Interconnect-   FPGA: Field Programmable Gate Areas-   SSD: solid-state drive-   IC: Integrated Circuit-   CU: Coding Unit

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof.

What is claimed is:
 1. A method for video decoding in a decoder,comprising: decoding coding information of a block to be reconstructedfrom a coded video bitstream, the coding information indicating intraprediction information for the block; and for the block coded with adirectional mode, determining the directional mode based on a nominalmode and an angular offset, the coding information indicating thenominal mode and the angular offset, determining a non-separabletransform for the block based on the nominal mode, and reconstructingthe block based on the directional mode and the non-separable transform.2. The method of claim 1, wherein the determining the non-separabletransform further comprises: determining a transform set mode that isassociated with the nominal mode, the transform set mode indicating aset of one or more non-separable transforms that includes thenon-separable transform.
 3. The method of claim 2, wherein the codinginformation further indicates a non-separable transform index; and thereconstructing the block further includes: determining the non-separabletransform in the set of one or more non-separable transforms based onthe non-separable transform index; and reconstructing the block based onthe directional mode and the non-separable transform.
 4. The method ofclaim 3, wherein the non-separable transform is a non-separablesecondary transform.
 5. The method of claim 4, wherein the non-separablesecondary transform does not apply to at least one of a PAETH mode and arecursive filtering mode.
 6. The method of claim 4, wherein thereconstructing the block based on the directional mode and thenon-separable secondary transform further comprises: applying thenon-separable secondary transform only to first N transform coefficientsalong a scanning order used for entropy coding the first transformcoefficients of the block.
 7. The method of claim 4, wherein thereconstructing the block based on the directional mode and thenon-separable secondary transform further comprises: applying thenon-separable secondary transform only to first transform coefficientsin the block, each of the first transform coefficients having acoordinate (x, y) and a sum of the respective x and y coordinates beingless than a threshold value.
 8. The method of claim 4, wherein ahorizontal transform and a vertical transform in a primary transform forthe block are included in a subset of a set of line graph transforms. 9.The method of claim 4, wherein the block includes first transformcoefficients obtained with the non-separable secondary transform andsecond transform coefficients obtained without the non-separablesecondary transform; and the reconstructing the block further includesentropy decoding the first transform coefficients and the secondtransform coefficients separately.
 10. The method of claim 1, whereinnon-directional modes include a DC mode, a PAETH mode, a SMOOTH mode, aSMOOTH_V mode, a SMOOTH_H mode, recursive filtering modes, and a chromafrom luma (CfL) mode, the DC mode, the PAETH mode, the SMOOTH mode, theSMOOTH_V mode, and the SMOOTH_H mode being based on averaging ofneighboring samples of the block, and for the block coded with one ofthe non-directional modes, determining a set of one or morenon-separable transforms associated with the one of the non-directionalmodes, one of (a) at least another one of the non-directional modes and(b) a nominal mode being associated with the set of one or morenon-separable transforms, determining a non-separable transform in theset of one or more non-separable transforms based on a non-separabletransform index indicated by the coding information, and reconstructingthe block based on the non-directional mode and the non-separabletransform.
 11. The method of claim 10, wherein the one of thenon-directional modes and the one of the at least another one of thenon-directional modes and the nominal mode include one of (a) therecursive filtering modes and one of the DC mode and the SMOOTH mode,(b) the SMOOTH mode, the SMOOTH_H mode, and the SMOOTH_V mode, (c) theSMOOTH mode, the SMOOTH_H mode, the SMOOTH_V mode, and the PAETH mode,(d) the recursive filtering modes, the SMOOTH mode, and the PAETH mode,(e) a vertical mode for the nominal mode and the SMOOTH_V mode, (f) ahorizontal mode for the nominal mode and the SMOOTH_H mode, and (v) theCfL mode and one of the DC mode, the SMOOTH mode, and the PAETH mode.12. An apparatus for video decoding, comprising processing circuitryconfigured to: decode coding information of a block to be reconstructedfrom a coded video bitstream, the coding information indicating intraprediction information for the block; and for the block coded with adirectional mode, determine the directional mode based on a nominal modeand an angular offset, the coding information indicating the nominalmode and the angular offset, determine a non-separable transform for theblock based on the nominal mode, and reconstruct the block based on thedirectional mode and the non-separable transform.
 13. The apparatus ofclaim 12, wherein the processing circuitry is further configured to:determine a transform set mode that is associated with the nominal mode,the transform set mode indicating a set of one or more non-separabletransforms that includes the non-separable transform.
 14. The apparatusof claim 13, wherein the coding information further indicates anon-separable transform index; and the processing circuitry isconfigured to: determine the non-separable transform in the set of oneor more non-separable transforms based on the non-separable transformindex; and reconstruct the block based on the directional mode and thenon-separable transform.
 15. The apparatus of claim 14, wherein thenon-separable transform is a non-separable secondary transform.
 16. Theapparatus of claim 15, wherein the processing circuitry is configuredto: apply the non-separable secondary transform only to first Ntransform coefficients along a scanning order used for entropy codingthe first transform coefficients of the block.
 17. The apparatus ofclaim 15, wherein the processing circuitry is configured to: apply thenon-separable secondary transform only to first transform coefficientsin the block, each of the first transform coefficients having acoordinate (x, y) and a sum of the respective x and y coordinates beingless than a threshold value.
 18. The apparatus of claim 15, wherein ahorizontal transform and a vertical transform in a primary transform forthe block are included in a subset of a set of line graph transforms.19. The apparatus of claim 15, wherein the block includes firsttransform coefficients obtained with the non-separable secondarytransform and second transform coefficients obtained without thenon-separable secondary transform; and the processing circuitry isconfigured to entropy decode the first transform coefficients and thesecond transform coefficients separately.
 20. The apparatus of claim 12,wherein non-directional modes include a DC mode, a PAETH mode, a SMOOTHmode, a SMOOTH_V mode, a SMOOTH_H mode, recursive filtering modes, and achroma from luma (CfL) mode, the DC mode, the PAETH mode, the SMOOTHmode, the SMOOTH_V mode, and the SMOOTH_H mode being based on averagingof neighboring samples of the block, and for the block coded with one ofthe non-directional modes, the processing circuitry is configured to:determine a set of one or more non-separable transforms associated withthe one of the non-directional modes, one of (a) at least another one ofthe non-directional modes and (b) a nominal mode being associated withthe set of one or more non-separable transforms, determine anon-separable transform in the set of one or more non-separabletransforms based on a non-separable transform index indicated by thecoding information, and reconstruct the block based on thenon-directional mode and the non-separable transform.
 21. The apparatusof claim 20, wherein the one of the non-directional modes and the one ofthe at least another one of the non-directional modes and the nominalmode include one of (a) the recursive filtering modes and one of the DCmode and the SMOOTH mode, (b) the SMOOTH mode, the SMOOTH_H mode, andthe SMOOTH_V mode, (c) the SMOOTH mode, the SMOOTH_H mode, the SMOOTH_Vmode, and the PAETH mode, (d) the recursive filtering modes, the SMOOTHmode, and the PAETH mode, (e) a vertical mode for the nominal mode andthe SMOOTH_V mode, (f) a horizontal mode for the nominal mode and theSMOOTH_H mode, and (v) the CfL mode and one of the DC mode, the SMOOTHmode, and the PAETH mode.